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Mathematics

The sum of the length, breadth and height of a cuboid is 41 cm. If the length of its diagonal is 25 cm, then its total surface area is :

  1. 1050 cm2

  2. 1052 cm2

  3. 1054 cm2

  4. 1056 cm2

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Answer

Given,

Sum of sides : l + b + h = 41 cm.

Length of diagonal (d) = 25 cm.

We know that,

Diagonal of cuboid (d) = l2+b2+h2\sqrt{l^2 + b^2 + h^2}

⇒ 25 = l2+b2+h2\sqrt{l^2 + b^2 + h^2}

Squaring on both sides,

⇒ 252 = (l2+b2+h2)2(\sqrt{l^2 + b^2 + h^2})^2

⇒ 625 = l2 + b2 + h2

By formula,

(l + b + h)2 = l2 + b2 + h2 + 2(lb + bh + hl)

By substituting the values we get,

⇒ (41)2 = 625 + 2(lb + bh + hl)

⇒ 1681 = 625 + 2(lb + bh + hl)

⇒ 2(lb + bh + hl) = 1681 - 625

⇒ 2(lb + bh + hl) = 1056

Since, Total surface area of cuboid = 2(lb + bh + hl)

∴ Total surface area of cuboid = 1056 cm2.

Hence, option 4 is the correct option.

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